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in Problem solving
That looks like a variety of schumach tree, Rhus typhina.
It will grow a lot bigger than 5', given the chance. Those are all young saplings of a proper tree.
You could simply dig them all out. The roots are quite shallow. There may be a parent tree somewhere nearby. Or perhaps one has been cut down recently. That sort of mass sprouting often happens if a schumach tree has been cut down. Young saplings sprout up from the entire area that was formerly covered by its roots.
Spraying with a weedkiller containing glyphsphate is another option, such as Roundup. It takes several weeks to take effect.
Or you could cut the saplings down now, and then spray any regrowth with glyphosphate. That would mke your garden tidier for the moment. But that would still leave a mat of shallow roots, that you'd need to remove before you can grow anything else there. So you might as well dig them out now.
If using weedkiller, you need to be careful that your neighbour hasn't still got the parent tree. If you use a weedkiller on the saplings, it will damage the parent.